12x2-116x+198=0

Solution for 12x2-116x+198=0 equation:

12x^2-116x+198=0

a = 12; b = -116; c = +198;
Δ = b2-4ac
Δ = -1162-4·12·198
Δ = 3952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3952}=\sqrt{16*247}=\sqrt{16}*\sqrt{247}=4\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{247}}{2*12}=\frac{116-4\sqrt{247}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{247}}{2*12}=\frac{116+4\sqrt{247}}{24}
$